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Tuesday, September 20, 2011

Cuisenaire Rods for Big(ger) Kids

I’ve seen a lot of discussion online about whether Cuisenaire Rods are essential to a child’s math development. These are mostly from parents leaning towards classical education, whose kids may already be maxed out with Singapore Math, phonics, grammar, maybe a Latin program. And the truth is – you don’t NEED rods… but I am so, SO happy I brought them into our lives (here’s one of our first “classes” with them, from almost 2 years ago).

Having a way to see and touch and manipulate (hey, so THAT’S why they call them “manipulatives”) numbers is essential. As Ruth Beechick says, most parents and teachers push kids WAY too early into patterns of abstract thought that – while they may be able to function in those modes – they are ultimately not yet ready for or fluent in yet.

If I could say one thing I’ve learned about teaching math so far, it would be: don’t rush to put away the toys!

Although our rods are not a feature of every lesson these days, and don’t integrate as naturally into our current JUMP Math program as they would, say, into Miquon Math, I always keep them nearby just in case. (oh, alright; also because our house is TINY)

So today, when I saw that we’d be learning about volume, I backed up and – before I handed her the worksheet, I showed her how we have looked at linear measurement so far – length, width, height, but we haven’t actually seen how much SPACE something takes up. For that, you need to measure not just one dimension, but TWO. (that’s more than I told her)

I showed her how we could measure the height of Story of the World, or its width, but if we wanted to see how BIG it was, we would need to measure the whole surface of it. (okay, somebody shoot me – my explanation included not a word about height, volume, etc., so this is not truly how BIG the book is)

For Naomi, the rods are like an old friend. She used to argue that she didn’t need them, but now she gets happy and even relaxes a little: she’s back in familiar territory. Even without much practice lately, she instantly recognizes the numerical value of each length / colour, and can glance at a gap and know (uncannily accurately) whether she’ll need a 3 (light green) or a 4 (purple) to fill in the space. She can also figure out multiples very quickly – more quickly, I think, than she could double the actual numerals (ie two purple 4’s make 8).

First, we laid orange 10-rods over the entire book, filling in a light green one (3) to make up the “extra” space in the corner. Then, I replaced every TEN orange rods with a blue “100-rod” square. Suddenly, we both knew the area of the book’s cover at a glance:

2 x 100-rods, plus 7 x 10-rods, plus 1 x 3-rod = 273

(I’m doing it faster here than I did with her, and I didn’t get into the question of units – ie “square centimetres”)

After this, we moved on to a Miquon worksheet – deciding which of two groups of rods has “more wood” (ie a greater area). And only AFTER the Miquon sheet, did I hand her the actual worksheet for the day, which involved comparing areas. The JUMP Math book says to trace the rectangles, cut them out, and then compare them… which I think is actually a BAD instruction, because it doesn’t give any actual criteria for comparison; there are no steps or instructions to the kids to help them know how to compare rectangles of different dimensions.

Whereas figuring out which one “has more wood” is a simple two-step operation: 1) cover each rectangle with rods (the book is metric, so the rods fit perfectly); 2) line up the rods and see which one is longest.

In this example, the shape covered with GREEN rods is larger – and when the rods are laid out end-to-end, the answer becomes very obvious.

I really believe that not only seeing but feeling the intuitiveness of early math operations will help prevent a whole lot of confusion farther down the line. Just about every time the rods come out, including today, she comes up with a dozen things she wants to teach ME (sometimes, I cut her short a bit, and sometimes, I hear her out). The rods are like a magical cape that, with my daughter, at least, transforms her from what I think of as an average math-kid into the Amazing Superheroine of Arithmetic… in her own mind, at least.

Oh – she was indeed crying in the picture at the very top of the page. That was NOT from the rods. She just has a rather protracted cold and is more sniffly and prone to crying (over the last week) than I have ever seen her before. No idea why; I just hope it ends SOON. It’s taking us twice as long to get through everything, and that only makes her cry more… because, you know, it’s taking so long. I am willing to skip things that are causing her anguish, but the tears seem totally random and unrelated to whatever curriculum she’s sitting in front of. Luckily, they pass just as quickly as they arrive. So that’s why she’s crying in the picture, and why we kept going anyway. She finished with a smile on her face, I promise!

3 comments:

What a cool way to use the c-rods! I just bought some, and it's exciting to see all the fun ways they can be used to make math so touchable. I'm thinking that there were not enough toys in my math education. =]P